The king has ordered that Qatari pilgrims be allowed "to enter Saudi Arabia through the border crossing to do the pilgrimage," it said.
He even ordered that private jets belonging to Saudi airlines be sent to Doha airport "to bring all Qatari pilgrims on his expenses".
The crown prince emphasised the "historical relations between Saudi and Qatari people, and between the Saudi leadership and the royal family in Qatar", the statement added.
Qatari authorities last month accused Saudi Arabia of jeopardising the pilgrimage to Mecca by refusing to guarantee their pilgrims' safety.
Saudi Arabia and its Arab allies shut down air, maritime and land links with Qatar, and imposed economic sanctions, accusing Doha of supporting "terrorists" and of being too close to Iran.
Qatar denies the charges and has accused its Gulf neighbours of seeking to strangle its economy.
The tiny emirate with a population of 2.6 million, 80 percent of them foreigners, ranks as the world's richest on a per-capita basis, according to the International Monetary Fund.
It holds a staggering $330 billion in a sovereign wealth fund, with assets heavily invested abroad.